During Labour's time in office, a routine complaint from Conservatives – big and small "c" – was that children were prevented from doing competitive sport in schools. Behind the charge there often lay a belief that teachers, in thrall to "progressive" theories, opposed the competitive impulse on principle.

Wrong. The last government invested millions in school sport and put in place the structures to expand competition across the country. Everyone involved in the project considers it a success. It is a shame, then, that education secretary Michael Gove did not do more to consult those involved before scrapping it.

There is much in the system to arouse the suspicion of a dogmatic Conservative: the block grant; performance indicators; the fact that the whole thing was dreamed up by Labour. It all sounds a bit like top-down bureaucracy of the kind to which David Cameron is famously allergic.

The awkward caveat is that, in this particular instance, it works. Since SSPs became operational, the number of children involved in inter-school competition has increased by 1.63 million; the number involved in competition within schools has increased by 1.15 million. There have also been increases in the numbers of children volunteering in sports activities outside school. Under Labour, the proportion of children in state schools fulfilling the curriculum requirement of at least two hours' PE per week increased from 25% to 95%.

Meanwhile, schools that specialised in sport show higher than average improvements in other fields. The ancient wisdom that a healthy body promotes a healthy mind is borne out by the data. Besides, healthy bodies – especially young ones – are a public policy goal in their own right. So are the social benefits of giving teenagers something worthwhile to do with their time. Not surprisingly, the Department of Health is reported to be unhappy with the cut. Other senior ministers are hardly overjoyed.

Why has Mr Gove taken his axe to the SSP network? The first answer is simply that there is no money. The deficit will be reined in and, inevitably, some things that people like will be lost. But that is a reason to reduce the budget or look for alternative ways to fund the scheme – sponsorship or private sector partnership. Besides, George Osborne claimed in the spending review that the schools budget had been protected.

Mr Gove has not forgotten about sport completely. He is compensating children with a "Schools Olympics", currently expected to receive around £10m in funding, to coincide with the London 2012 Games. But this glorified sports day is no substitute for the SSP network, which could surely have been preserved on reduced means through the lean years, with a hope of revival when budget conditions improve.

The fate of the SSPs illustrates two unattractive traits of the coalition government.

The first is a tendency to put ideological impulse ahead of evidence. Mr Gove's communications with the SSP leadership, seen by the Observer, indicate that he objected to the centralised system on principle. The second is a sneaky approach to cuts. If schools want their pupils to continue enjoying SSP programmes, they must divert the money from other educational priorities. Ministers call this "setting schools free from Whitehall", which translates as "letting head teachers inflict the pain".

This is the reality of austerity. Not everything can be saved. But it would be easier to have confidence in ministers if they had the decency to look hard at something their predecessors built before blithely chopping it down.